Inertial frames are the tricky topic. They are NOT so hard to understand, but there seems NO short way to explicate them. One just has to grasp all their aspects at once in a big picture---and then they make sense---or so yours truly hopes.
Yours truly admits to having rewritten the discussion of them 10 times or more.
Here we give the somewhat abstract summary explication of inertial frames---which is longish---then in following file sections, we expand on it with diagrams and animations.
Note the term "local" is used variously in physics jargon. Here we mean at the same place or in the same COMMFI frame.
Note absolutely positively different COMMFI frame comoving frames are NOT local with respect to each other. Such frames are in "acceleration" with respect to each other in the expansion-of-the-universe motion, but are still inertial frames.
Any location on the surface of the Earth or any planet is an approximate inertial frame for most purposes. Thus, you can reference Newton's laws of motion to the ground for most purposes. But NOT for all purposes: see sections The Centrifugal Force of the Earth's Rotation The Coriolis Force of the Earth's Rotation below.
A key example physical law that must be referenced to inertial frames is that the vacuum light speed c = 2.99792458*10**5 km/s ≅ 2.998*10**5 km/s ≅ 3*10**5 km/s ≅ 1 ft/ns is the fastest physical speed relative to all local inertial frames including those that are effective inertial frames. This means acually all local observers measure the same vacuum light speed: it is invariant as well as fastest.
UNDER RECONSTRUCTION BELOW: everything is right I think, but there are repetitions
Note that unrotating with respect to the observable universe means that all inertial frames are unrotating with respect to each other.
If a reference frame is in acceleration relative to a free-fall frame or in rotation with respect observable universe (which is actually an accelerated motion), it is a non-inertial frame.
Well, you can just NOT use them and use inertial frames instead. There are always local inertial frames wherever you are.
On the other hand, you can convert non-inertial frames into inertial frames using special frame-dependent forces called inertial forces.
Inertial forces are sometimes called fictitious forces, but yours truly deprecates that term because inertial forces act just like gravity on sufficiently small scales. A key point is that inertial forces are linearly dependent on mass. just like gravity.
In fact, it is an axiom of general relativity that inertial forces and gravity have a fundamental likeness.
So using inertial forces is NOT a trick. It is a perspective that may be taken if it is convenient to do so. There are many important cases where it is convenient.
Our current cosmological paradigm of the expanding universe (which is general to almost all currently though-of cosmological theories including the favored Λ-CDM model) tells us that the bulk mass-energy of observable universe is NOT in rotation at least in any sense we normally understand by the term rotation.
Thus, we can say there is such a thing as absolute rotation: i.e., rotation relative to the observable universe.
How do we measure absolute rotation?
The accurate/precise way at present is relative to cosmologically remote quasars whose peculiar velocities relative to the mean expansion of the universe are believed to be negiligible from our perspective on Earth. Such measurements establish the International Celestial Reference Frame (ICRF).
However, at a lower, but often very adequate, level of accuracy/precision one can use the average array of the traditional fixed stars which are just the stars that you see at night. The array of fixed stars do actually have some absolute rotation, but for most, but NOT all, purposes it is negligible.
Before the advent of modern cosmology (circa 1900--1930) rotation relative to the array of fixed stars was taken as an exact measure absolute rotation by most astronomers. Of course, the fixed stars individually were known or assumed to have peculiar velocities since the time of Isaac Newton (1643--1727), but on average they were thought to be at rest in absolute space.
Note that many people and yours truly occasionally say "relative to the fixed stars" as a synonym for relative to the observable universe. This is just a traditional usage and yours truly is trying to get out of the habit of using it.
Absolute space was hypothesized by Isaac Newton (1643--1727) to be the fundamental inertial frame (and the one in which the fixed stars [which were all the stars in his age] were at rest on average) and only reference frames NOT accelerated with respect to it were true inertial frames.
Now yours truly likes the perspective that Newtonian physics is a true emergent theory. It is exactly true in the classical limit.
But NOT absolute space. That was always a wrong hypothesis.
However, practitioners of celestial mechanics assuming absolute space from Newton on until the advent of general relativity in 1915 and even a bit later (see below) still got the right answers for calculations of celestial motions of the Solar System and observable multiple star systems. Why?
They used the fixed stars for defining absolute rotation (as we discussed in section What Do We Mean by Rotation With Respect to the Observable Universe?) and that was adequate for their level of accuracy/precision. They then treated the free-fall frames defined by the centers of mass of their systems unrotating relative to the fixed stars as non-inertial frames converted to inertial frames by the use of inertial forces. This procedure as far as the celestial motions they were dealing with gives exactly the right answers since converted non-inertial frames are also inertial frames.
Now Newton and those other old practitioners of celestial mechanics could equally well have anticipated the general relativity perspective of free-fall frames unrotating with respect to the observable universe (which for them was the fixed stars) all being true inertial frames (unneeding of any conversion using inertial forces), but they did NOT do so.
General relativity, of course, tells us that its perspective on inertial frames is the correct one for the observable universe.
The theory of absolute space continued to be held by some up to the 1920s. The observational discovery of the expanding universe in 1929 by Edwin Hubble (1889--1953) and its theoretical understanding in terms of the Friedmann-equation (FE) models derived from general relativity caused absolute space to be thoroughly and most sincerely discarded.
So there is NO absolute space in the sense used by Newton. What is there instead?
Free-fall frames unrotating with respect to the observable universe and participating the mean expansion of the universe are now considered the most basic inertial frames or the most fundamental inertial frames.
The centers of mass of most galaxy groups and clusters and most field galaxies define inertial frames that are good approximations to comoving frames: i.e., they coincide approximately with exact comoving frames.
Furthermore on comoving frames, there are two fine points:
Because the two dark energy forms act the same in the Friedmann-equation (FE) models, they are, as a shorthand, often just collectively referred to as Lambda since the capital Greek letter Λ (pronounced Lambda) is the symbol for the cosmological constant.
It may be the neither of the two dark energy forms are the true cause of acceleration of the universe. Hopefully, we will find the true cause someday.
The cosmological constant Λ (or whatever is causing the acceleration of the universe) is usually unimportant on scales much less than that of the observable universe and is NOT usually mentioned unless it is of importance to an analysis.
In fact, we can measure our local motions relative to our local comoving frame to good accuracy/precision by measurement of the cosmic microwave background (CMB).
The CMB is just electromagnetic radiation (EMR) in the microwave band (fiducial range 0.1--100 cm). It strongest in the energy/frequency/wavelength bands ∼ 1--22 cm and has one of the most perfect blackbody spectra found in nature (see Wikipedia: Cosmic microwave background: Features). It is a relic of the Big Bang era speaking loosely. It permeates the observable universe and, according to Big Bang cosmology (which is highly trusted), it is isotropic when viewed in a comoving frame.
We will NOT elaborate on the CMB here. But we can give some local velocities determined using it: